The Parts and Wholes of Arithmetic Story Problems: Developing Knowledge in the Preschool Years

Sophian, Catherine; Vong, Keang Ieng Peggy

doi:10.1207/s1532690xci1303_5

Cited by 26 publications

(19 citation statements)

References 3 publications

(6 reference statements)

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“…The results show that in addition to using concrete or graphical analogues to solve symbolic problems (Alexander et al, 1997;English, 1997;English & Sharry, 1996;Singer-Freeman & Goswami, 2001;Sophian & Vong, 1995;Sophian & Wood, 1997;Spinillo & Bryant, 1991, 1999, young children can engage in reasoning about conceptual relations within the domain of addition based on the correspondences between separate problems. In the study, children used the mathematical concept of commutativity to judge two arithmetic problems as related.…”

Section: Discussionmentioning

confidence: 98%

The role of relational reasoning in children's addition concepts

Farrington-Flint

Canobi

Wood

et al. 2007

British J of Dev Psycho

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The study addresses the relational reasoning of different‐aged children and how addition reasoning is related to problem‐solving skills within addition and to reasoning skills outside addition. Ninety‐two 5‐ to 8‐year‐olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all self‐reported strategies were used to monitor their addition performance. Children were also given a series of general relational reasoning tasks to assess their ability to solve problems based on thematic, causal and visual relations. The results revealed that, while children were able to reason about commutativity relations, recognition of relations based on additive composition was rare. Furthermore, children's ability to reason about addition concepts increased with age and problem‐solving proficiency. Reasoning about addition concepts was related to performance on the thematic, causal and visual reasoning tasks for older children but not for younger children. Overall, the findings suggest that while children's early knowledge of addition relations is domain specific, as children develop in their broader reasoning abilities these developments enhance their addition reasoning.

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Section: Discussionmentioning

confidence: 98%

The role of relational reasoning in children's addition concepts

Farrington-Flint

Canobi

Wood

et al. 2007

British J of Dev Psycho

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“…For example, there is abundant literature supporting the role of children’s cognitive abilities in school readiness (Bickham et al, 2001; Duncan et al, 2007), in particular executive functions (e.g., Riggs, Blair, & Greenberg, 2003; Zelazo, Carter, Reznick, & Frye, 1997), preliteracy (e.g., Hart & Risley, 1999; Jordan, Snow & Porche, 2000; Whitehurst & Lonigan, 1998,) and prenumeracy skills (e.g., Sophian & Vong, 1995). Thus, when examining links between social cognitions and aspects of school readiness, one must carefully consider the types of school readiness factors that are most likely to be influenced by these social cognitive processes.…”

Section: Social Information Processing Patterns Social Skills and Smentioning

confidence: 99%

Social information processing patterns, social skills, and school readiness in preschool children

Ziv

2013

Journal of Experimental Child Psychology

116

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The links between social information processing, social competence, and school readiness were examined in this short-term longitudinal study with a sample of 198 preschool children. Data on social information processing were obtained via child interview, data on child social competence were obtained via teacher report, and data on school readiness were obtained via child assessment (early literacy skills) and teacher report (approaches to learning). Findings provided support for our hypothesis that both social information processing and social competence are related to school readiness. Social competence also partially mediated the link between social information processing and school readiness thus supporting our hypothesis about an indirect path in which mental processes are translated into social skills and then translated into school readiness.

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“…These are situations involving a change from an initial to a final state through the application of a transformation (change problems), the combination of two discrete sets or splitting of one set into two discrete sets (combine problems) and the quantified comparison of two discrete sets of objects (compare problems). Within each of these three major semantic categories, further distinctions were made resulting in 18 different types of one‐step addition and subtraction problems (Riley, Greeno, & Heller, 1983; see also Fuson, 1992; Reed, 1999; Riley & Greeno, 1988; Verschaffel & De Corte, 1993, 1997).…”

Section: Rewordings Used In Previous Studiesmentioning

confidence: 99%

“…The criteria for rewording the problems were based on some of the theoretical positions described earlier. For conceptual rewording, we followed Riley et al 's (1983; Riley & Greeno, 1988) idea that understanding the semantic relations described by the text depends on understanding part‐whole relations, especially for more difficult problems. Therefore, our conceptual reformulations of the two‐step change problems make explicit the conceptual role of the total set shared by the two one‐step change situations (i.e.…”

Section: Studymentioning

confidence: 99%

“…An interesting feature of this type of conceptual rewording is that, contrary to previous studies wherein every kind of rewording was tied to a specific kind of problems, it can be applied to all problem types. After all, applying part‐whole knowledge is needed for solving all (difficult) kinds of addition and subtraction problems (Riley & Greeno, 1988; Riley et al , 1983). Regarding situational rewording, we took Reusser's (1985, 1990) situation problem solving (SPS) model as theoretical frame, because it is the only one that involves the generation of an episodic situation model, implying ‘the application of comprehension strategies to the text base, which generate an analysis of the temporal and functional structure of the situations and actions depicted in the problem text’ (Staub & Reusser, 1995, p. 293).…”

Section: Studymentioning

confidence: 99%

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